2013 AMC 12B Problem 11

Two bees start at the same spot and fly at the same rate in the following directions. Bee A travels 1 foot north, then 1 foot east, then 1 foot upwards, and then continues to repeat this pattern. Bee B travels 1 foot south, then 1 foot west, and then continues to repeat this pattern. In what directions are the bees traveling when they are exactly 10 feet away from each other?

\textbf{(A)}\ A east, B west
\textbf{(B)}\ A north, B south
\textbf{(C)}\ A north, B west
\textbf{(D)}\ A up, B south
\textbf{(E)}\ A up, B west

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.